Markov Diagrams

Markov diagrams allow you to model the behavior of systems based on transitions between states, where the next state that the system enters is dependent only upon the current state (and not affected by any previous states). This gives you the ability to look at partial or degraded working states, and to start analysis in varying states.

Markov diagrams may be:

• Discrete - At the end of a given step, the system will transition to another state (or remain in the current state), based on fixed probabilities. Appropriate for general probabilities, genetics, physics, etc.
• Continuous - The time of state transition is unknown; therefore, the rate is determined from exponential probability models. Appropriate for examining system reliability.

In both discrete and continuous diagrams, you can use phases to represent situations where the transitions between states change over time.

Building a Markov Diagram - An Overview

The basic steps for creating a Markov diagram that is ready for analysis are as follows:

1. Add a state block for each possible state.
2. Define the initial probability that the system will be in each state at the start of analysis. The sum of the initial probabilities for all states must equal 1.
3. Connect the blocks to show the possible transitions between states.
4. For each transition, define the conditions under which the system moves from the source state to the target state (fixed probability of occurrence for a discrete diagram, exponential distribution representing the rate at which the change happens for a continuous diagram).
5. Specify how long the analysis will run (number of steps for a discrete diagram, length of time for a continuous diagram).
6. If you are using phases:
   1. Create a diagram for each additional phase.
   2. Specify the order of the phases.
   3. Specify the overall length of the analysis.

Most of the techniques for working with objects in a Markov diagram, such as selecting blocks within the diagram, copying/pasting blocks and arranging blocks, are the same as the options described for RBDs and fault trees. For information on modifying appearance settings, see Diagram Skins and Appearance Settings.

For more detailed information on using each diagram type, see Discrete Markov Diagrams and Continuous Markov Diagrams. For information about using phases, see Phases in Markov Diagrams.